CN105550424A - Screening method of interpolating sequences based on RBF grid deformation - Google Patents

Abstract

The invention belongs to the technical field of numerical simulation of computational grid generation of computational fluid mechanics, and specifically relates to a screening method of interpolating sequences based on RBF grid deformation. The method comprises the following steps of: 1, building a RBF grid deformation module; 2, screening initial interpolating sequences; 3, calculating an interpolation error; 4, searching an extremum value of the interpolation error delta i through an extremum algorithm; 5, screening a RBF interpolating sequence. In the method provided by the invention, efficiency of screening the interpolating sequences is improved by means of combination of the extremum algorithm and a greedy algorithm, the extremum value of the interpolation error is searched in screening iteration, an extremum value point of which the error is greater than a threshold value is screened and added into the sequence, and thus, fast simplification of the radial basis function interpolating sequences is realized.

Description

A kind of screening technique based on RBF distortion of the mesh interpolating sequence

Technical field

The invention belongs to Computational fluid mechanics numerical simulation computing grid generation technique field, be specifically related to a kind of screening technique based on RBF distortion of the mesh interpolating sequence.

Background technology

Computing grid robotization generation is the importance of the numerical simulation pre-treatments such as flight vehicle aerodynamic configuration design optimization, aeroelasticity, at present, and the normal automatic generation adopting mesh deformation technique to realize optimizing configuration and gas bullet distortion body fitted grids in engineer applied.Mesh deformation technique, by carrying out translation, rotation and torsional deflection operation to computing grid, under the conforming prerequisite of network topology, enables computing grid accurately reflect the change of shape of aircraft.From several aspects comparative analyses such as grid applicability, deformability, deformation efficiency, texturing quality, algorithm complexes, carrying out distortion of the mesh based on RBF interpolation is the good grid deforming method of integration capability, in recent years obtain fast development, and be successfully applied in elastic body Pneumatic Calculation distortion of the mesh analysis.

Based on calculated amount and the N of RBF distortion of the mesh _spbecome duplicate ratio relation, memory consumption and N _spbecome cube than relation, N in base _spbe the basic point number of the Interpolation Property of Radial Basis Function sequence of carrying out interpolation, its magnitude is generally 10 ⁴~ 10 ⁶.For the 3D grid that grid node number is more, directly very large for RBF interpolating sequence carries out distortion of the mesh calculated amount with net point on all deformation boundaries faces.In order to improve distortion of the mesh counting yield, the memory consumption in Reducing distortion, must simplify RBF interpolating sequence.Often adopt greedy algorithm to the screening of RBF interpolating sequence at present, its algorithm idea will occur that the point of maximum error is brought in interpolating sequence in screening iteration, thus screening obtains little as far as possible N under the prerequisite meeting interpolation precision _sp.Screening process iteration of greedy algorithm only adds a node to interpolating sequence, and error convergence speed is slow, and screening process may need to screen iteration many times.

Summary of the invention

Large in order to solve the calculated amount of distortion of the mesh in background technology, the slow-footed problem of error convergence of greedy algorithm screening RBF interpolating sequence, the present invention proposes one and can accelerate interpolation error speed of convergence, improve the screening technique based on RBF distortion of the mesh interpolating sequence of interpolating sequence screening effeciency.

Concrete technical scheme of the present invention is:

Based on a screening technique for RBF distortion of the mesh interpolating sequence, it is characterized in that, comprise the following steps:

1) RBF distortion of the mesh module is built:

2) initial interpolating sequence is screened

Setting initial mesh deformation boundaries face S, arbitrary mess node is chosen in initial mesh deformation boundaries face, as the basic point P of the initial radial base interpolating sequence of RBF distortion of the mesh module ₀={ p ₁, p ₂..., p _m; M represents the number of the basic point of initial radial base interpolating sequence

3) run RBF distortion of the mesh module, obtain the second distortion of the mesh boundary surface S ₁, calculate the interpolation error S on the second distortion of the mesh boundary surface and initial mesh deformation boundaries _i;

4) extreme value algorithm search interpolation error δ is adopted _iextreme value

4.1) initial mesh deformation boundaries face is divided into N number of region of search Ω _i

4.2) each region of search Ω is searched for _imaximum error

${\mathrm{\δ}}_{{\mathrm{\Ω}}_i}=\underset{p_k\∈{\mathrm{\Ω}}_i}{\max }({\mathrm{\δ}}_1,{\mathrm{\δ}}_2,\mathrm{...},{\mathrm{\δ}}_k)$

Wherein k represents search Ω _ithe number of interior interpolation error;

Complete N number of region of search Ω _iextremum search, define a series of extreme value

5) RBF interpolating sequence is screened

5.1) step-up error threshold values σ, σ are 10 of initial mesh deformation boundaries face maximum deformation quantity ^-3

5.2) selecting step 4.2) extreme value that formed in any one if

$\left|{\mathrm{\δ}}_{{\mathrm{\Ω}}_i}\right|>\mathrm{\σ}$

Then remember appearance region of search on node be p _m+i;

If

$\left|{\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}\right|<\mathrm{\&sigma;}$

Then filtering occurs region of search;

5.3) if p _m+iwith initial radial base interpolating sequence P ₀basic point repeat, then filtering; Otherwise carry out step 5.4)

5.4) if p _m+ithe basic point P of initial radial base interpolating sequence ₀adjacent node, then filtering; Otherwise retain p _m+i

5.5) step 5.2 is repeated) to 5.4) filter out extreme value point range p _m+1..., p _m+s, according to the principle of greedy algorithm, form new radial base interpolation sequence

P ₁={ p ₁, p ₂..., p _m, p _m+1..., p _m+s, behalf step 5.2) to 5.4) the middle node number inserting initial radial base interpolating sequence;

6) according to step 5.5) the radial base interpolation sequence that formed, repeat step 3) to step 5), until all extreme values all be not more than given error threshold values σ, then screening process terminates.

Above-mentioned RBF distortion of the mesh module is used for the input of distortion of the mesh controling parameters, the input of initial calculation grid, creates deformation boundaries face, creates distortion of the mesh region, creates Initial R BF interpolating sequence.

The invention has the advantages that:

Adopt method of the present invention in the iteration of screening radial basis function interpolating sequence, error convergence speed is fast, and screening effeciency is high, realizes simplifying fast of Interpolation Property of Radial Basis Function sequence.This method screens the radial base interpolation sequence obtained, and can ensure the interpolation precision of distortion of the mesh, has significantly reduced the number of the calculated amount of distortion of the mesh simultaneously, for shortening Flight Vehicle Design optimization and aeroelasticity numerical simulation cycle provide technical support.

Accompanying drawing explanation

Fig. 1 is Interpolation Property of Radial Basis Function sequence screening process flow diagram of the present invention

Embodiment

Under the requirement meeting interpolation precision, simplify RBF interpolating sequence be reduce RBF distortion of the mesh calculated amount most important technological means.On initial interpolating sequence basis, by deformation boundaries face being screened the basic point of the large node of RBF distortion of the mesh interpolation error as sequence, reduce interpolation error amount gradually, until reach the error precision of setting.Method of the present invention is intended to accelerate error convergence speed, improves RBF distortion of the mesh iteration screening effeciency, establishes the interpolating sequence screening technique of extreme value algorithm in conjunction with greedy algorithm.

Specific descriptions below in conjunction with accompanying drawing 1 pair of the inventive method are as follows:

1) RBF distortion of the mesh module is built;

Wherein, RBF distortion of the mesh module grid is used for Deformation control parameters input, the input of initial calculation grid, creates deformation boundaries face, creates distortion of the mesh region, creates Initial R BF interpolating sequence etc., provides necessary pretreatment information for distortion of the mesh calculates.

Specifically:

Distortion of the mesh controling parameters main definitions is:

◆ the type of definition distortion of the mesh, comprises Grid Mobile, rotation, torsional deflection and aggregate motion distortion thereof.

◆ definition grid rotates, moving movement form.

◆ deflection, the form of distortion of the data point of definition distortion of the mesh.

◆ definition distortion of the mesh restricted area.

Initial calculation grid is input as:

◆ the net point coordinate of input initial calculation grid.

◆ input initial mesh network topology and boundary information.

Creating deformation boundaries face is:

◆ the boundary surface of initial calculation grid is created according to distortion of the mesh controling parameters.

◆ the deformation boundaries face of distortion of the mesh is created according to distortion of the mesh controling parameters.

◆ for grid torsional deflection, carry out geometric parameter modeling.

Creating distortion of the mesh region is:

◆ in initial mesh, create distortion of the mesh region according to distortion of the mesh controling parameters, simplify grid scale to be deformed in computational fields.

Creating Initial R BF interpolating sequence is:

◆ according to network topology and net point distribution, choose node on deformation boundaries as basic point.Create Initial R BF interpolating sequence.

◆ create RBF interpolating sequence file, initial interpolating sequence is outputted to file.

2) initial interpolating sequence is screened; For the interpolating sequence chosen, the net point displacement of sequence basic point is accurate, and the net point displacement of non-sequence basic point is obtained by RBF method interpolation, there is interpolation error.By increasing the basic point number of interpolating sequence, reduce error amount gradually, specific practice is:

Setting initial mesh deformation boundaries face S, arbitrary mess node is chosen in initial mesh deformation boundaries face, as the basic point P of the initial radial base interpolating sequence of RBF distortion of the mesh module ₀={ p ₁, p ₂..., p _m; M represents the number of the basic point of initial radial base interpolating sequence

3) run RBF distortion of the mesh module, obtain the second distortion of the mesh boundary surface S ₁, calculate the interpolation error δ on the second distortion of the mesh boundary surface and initial mesh deformation boundaries _i;

4) extreme value algorithm search interpolation error δ is adopted _iextreme value

4.1) initial mesh deformation boundaries face is divided into N number of region of search Ω _i

4.2) each region of search Ω is searched for _imaximum error

${\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}=\underset{p_k\&Element;{\mathrm{\&Omega;}}_i}{\max }({\mathrm{\&delta;}}_1,{\mathrm{\&delta;}}_2,\mathrm{...},{\mathrm{\&delta;}}_k)$

Wherein k represents search Ω _ithe number of interior interpolation error;

Complete N number of region of search Ω _iextremum search, define a series of extreme value

5) RBF interpolating sequence is screened: this step determines whether whether added in RBF interpolating sequence by the extreme point that a program module upper in flow process is selected.Screening mode comprises threshold values screening, repeats a screening and isolatism screening.Then the node of the appearance extreme value satisfied condition to be added in existing RBF interpolating sequence and to carry out error convergence judgement.

5.1) step-up error threshold values σ, σ are 10 of initial mesh deformation boundaries face maximum deformation quantity ^-3

5.2) selecting step 4.2) extreme value that formed in any one if

$\left|{\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}\right|>\mathrm{\&sigma;}$

Then remember appearance region of search on node be p _m+i;

If

$\left|{\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}\right|<\mathrm{\&sigma;}$

Then filtering occurs region of search;

5.3) if p _m+iwith initial radial base interpolating sequence P ₀basic point repeat, then filtering; Otherwise carry out step 5.4)

5.4) if p _m+ithe basic point P of initial radial base interpolating sequence ₀adjacent node, then filtering; Otherwise retain p _m+i

5.5) step 5.2 is repeated) to 5.4) filter out extreme value point range p _m+1..., p _m+s, according to the principle of greedy algorithm, form new radial base interpolation sequence

P ₁={ p ₁, p ₂..., p _m, p _m+1..., p _m+s, behalf step 5.2) to 5.4) the middle node number inserting initial radial base interpolating sequence

6) according to step 5.5) the radial base interpolation sequence that formed, repeat step 3) to step 5), until all extreme values all be not more than given error threshold values σ, then screening process terminates.

Claims (2)

1. based on a screening technique for RBF distortion of the mesh interpolating sequence, it is characterized in that, comprise the following steps:

1) RBF distortion of the mesh module is built:

2) initial interpolating sequence is screened

Setting initial mesh deformation boundaries face S, arbitrary mess node is chosen in initial mesh deformation boundaries face, as the basic point P of the initial radial base interpolating sequence of RBF distortion of the mesh module ₀={ p ₁, p ₂..., p _m; M represents the number of the basic point of initial radial base interpolating sequence

3) run RBF distortion of the mesh module, obtain the second distortion of the mesh boundary surface S ₁, calculate the interpolation error δ on the second distortion of the mesh boundary surface and initial mesh deformation boundaries _i;

4) extreme value algorithm search interpolation error δ is adopted _iextreme value

4.1) initial mesh deformation boundaries face is divided into N number of region of search Ω _i

4.2) each region of search Ω is searched for _imaximum error

${\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}=\underset{p_k\&Element;{\mathrm{\&Omega;}}_i}{\max }({\mathrm{\&delta;}}_1,{\mathrm{\&delta;}}_2,\mathrm{...},{\mathrm{\&delta;}}_k)$

Wherein k represents search Ω _ithe number of interior interpolation error; Complete N number of region of search Ω _iextremum search, define a series of extreme value

5) RBF interpolating sequence is screened

5.1) step-up error threshold values σ, σ are 10 of initial mesh deformation boundaries face maximum deformation quantity ^-3

5.2) selecting step 4.2) extreme value that formed in any one

If

$\left|{\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}\right|>\mathrm{\&sigma;}$

Then remember appearance region of search on node be p _m+i;

If

$\left|{\mathrm{\&delta;}}_{{\mathrm{\&Omega;}}_i}\right|<\mathrm{\&sigma;}$

Then filtering occurs region of search;

5.3) if p _m+iwith initial radial base interpolating sequence P ₀basic point repeat, then filtering; Otherwise carry out step 5.4)

5.4) if p _m+ithe basic point P of initial radial base interpolating sequence ₀adjacent node, then filtering; Otherwise retain p _m+i;

5.5) step 5.2 is repeated) to 5.4) filter out extreme value point range p _m+1..., p _m+s, according to the principle of greedy algorithm, form new radial base interpolation sequence

P ₁={ p ₁, p ₂..., p _m, p _m+1..., p _m+s, behalf step 5.2) to 5.4) the middle node number inserting initial radial base interpolating sequence;

6) according to step 5.5) the radial base interpolation sequence that formed, repeat step 3) to step 5), until all extreme values all be not more than given error threshold values σ, then screening process terminates.

2. the screening technique based on RBF distortion of the mesh interpolating sequence according to claim 1, it is characterized in that: described RBF distortion of the mesh module is used for the input of distortion of the mesh controling parameters, the input of initial calculation grid, creates deformation boundaries face, creates distortion of the mesh region, creates Initial R BF interpolating sequence.